As is known, LEDs find increasing application in the automotive field on account of the intrinsic advantages associated to use thereof, such as, for example: reduced power consumption, contained weight, limited overall dimensions, high reliability, average service life longer than that of normal lamps, attractive design, low thermal emission, and possibility of modulating the light intensity emitted by the LEDs.
As regards this latter aspect, it is known to carry out control of brightness of LEDs by supplying thereto a current having a rectangular waveform and adjusting the time width (duration) of the rectangular pulses by means of a PWM (Pulse-Width Modulation) control. Use of a PWM control enables operation of the LEDs in an operating area in which the duration is maximized and the thermal emission is further reduced.
For example, the patent application DE 10 2008 027 148 filed in the name of TechnisSat Digital GmbH describes a vehicle lighting device, in particular a rear brake light, in which at least three sets of LEDs belonging to respective circuit branches are supplied through switches switched by means of respective first, second, and third driving signals having a rectangular waveform and constant frequency. Each waveform is phase-offset with respect to the other waveforms in such a way that, globally, the various LEDs are lit up in time intervals that are substantially contiguous (the falling edge of one rectangular pulse coincides with or is close to the rising edge of a rectangular pulse of another waveform—see FIG. 4 of the patent application DE 10 2008 027 148) in order to provide a “practically continuous” lighting effect that improves the perception by the human eye of the light produced by the lighting device.
The phase offset of the various waveforms with respect to one another is obtained by applying a phase difference that is an integer multiple N·Tf of a common phase difference Tf between the various waveforms. In this way, the current It globally supplied to the various sets of diodes is given by the following expression:It=i(t)+i(t−Tf)+i(t−2Tf), . . . ,i(t−NTf)where i(t)+i(t−Tf)+i(t−2Tf), . . . , i(t−NTf) are the pulsating currents supplied to each branch. The terms i(t), i(t−Tf), i(t−2Tf), . . . , i(t−NTf) have a rectangular waveform.
In other words, the temporal spacing between one waveform and the next is constant (Tf).
The current globally supplied to the LEDs is variable in time, and the frequency spectrum of said current is other than zero for frequencies higher than zero.
In order to compute the frequency spectrum, it is necessary to compute the Fourier transform of the function i(t), recalling that the Fourier transform of the boxcar function is the sin c(f) function.
Since the signal is periodic, its spectrum N′ (f) is given by the sum of sin c(f) functions for the various boxcar functions and a phase given by the sum of the phases e−j2πfti (or phasors), i.e.
            N      ′        ⁡          (      f      )        =            ∑              i        =        0            2        ⁢                  ⁢          sin      ⁢                          ⁢                        c          ⁡                      (            f            )                          ·                  ⅇ                                    -              j2π                        ⁢                                                  ⁢            fti                              
By extracting the real part from the summation, we obtain:
            N      ′        ⁡          (      f      )        =      sin    ⁢                  ⁢                  c        ⁡                  (          f          )                    ·                        ∑                      i            =            0                    2                ⁢                                  ⁢                  ⅇ                                    -              j2π                        ⁢                                                  ⁢            fti                              
The presence of a non-zero frequency spectrum inevitably entails generation of a disturbance that may be transmitted in a conducted or radiated way and that may be potentially dangerous in so far as it interferes with other electronic devices provided on the vehicle. In particular, in the case of the patent illustrated above, it may be shown mathematically how the phasors add up; for this reason, the absolute value of the summation of the phasors
              ∑              i        =        0            2        ⁢                  ⁢          ⅇ                        -          j2π                ⁢                                  ⁢        fti              is equal to the number of branches.
The time spacing between the driving signals and the waveforms envisaged according to the known art (patent application DE 10 2008 027 148) consequently represents the spacing that concurs in maximizing electromagnetic disturbance.